System and method for automatic construction of orthodontic reference objects

ABSTRACT

System and method for automatic construction of orthodontic reference objects, such as the occlusal plane, arch form, and the local occlusal plane for a patient&#39;s teeth are disclosed. In accordance with an exemplary embodiment, a computer-implemented system and method for automatic construction of orthodontic reference objects comprises receiving three dimensional data for the teeth, setting an initial direction for a normal of the occlusal plane, determining tips for selected teeth, calculating a plane that matches the determined tip, and determining a new normal for the calculated plane.

FIELD OF INVENTION

The present invention relates generally to the field of orthodontics,and in particular to system and method for automatic construction oforthodontic reference objects.

BACKGROUND OF THE INVENTION

One objective of orthodontics is to move a patient's teeth to positionswhere the teeth function optimally and are also aesthetically pleasing.Conventional appliances such as braces and wires are applied to theteeth of a patient by an orthodontist. Once mounted on the teeth, thebraces exert continual force on the teeth and gradually urge the teethto their respective ideal position. The orthodontist does this byadjusting the braces over time to move the teeth toward their finaldestination.

Orthodontic brackets are often bonded directly to the patient's teeth.Typically, a small quantity of adhesive is placed on the base of eachbracket and the bracket is then placed on a selected tooth. Before theadhesive is set, the bracket is maneuvered to a desired location on thetooth. Once the adhesive has hardened, the bracket is bonded to thetooth with sufficient strength to withstand subsequent orthodonticforces as treatment progresses. One shortcoming with this technique isthe difficulty in accessing the optimal surface for bracket placement onseverely crowded teeth or in teeth where the bonding surface isobstructed by teeth in the opposing arch during jaw closure. Withposterior teeth, the treatment provider may have difficulty seeing theprecise position of the bracket relative to the tooth surface. Theamount of time needed to carry out the bonding procedure may be anuisance both to the patient as well as to the treatment provider. Also,the necessity of minimizing moisture contamination from the patient'ssaliva can prolong the procedure and also unduly impair the accuracy ofplacement of the brackets on the teeth. All of these factors increasethe chance that one or more brackets will be incorrectly positioned onthe teeth.

Apparatus, systems, and methods have been developed to facilitate teethmovement utilizing clear, removable teeth aligners as an alternative tobraces. A mold of the patient's bite is initially taken and desiredending positions for the patient's teeth (i.e., a functionally andaesthetically optimum position) are determined, based on a prescriptionprovided by an orthodontist or dentist. Corrective paths between theinitial positions of the teeth and their desired ending positions arethen planned. These corrective paths generally include a plurality ofintermediate positions between the initial and ending positions of theteeth.

Multiple clear, removable aligners formed to move the teeth to thevarious positions along the corrective path are then manufactured. Onesystem for providing such aligners is the Invisalign® System from AlignTechnologies, Inc. of Santa Clara, Calif.

The planning of the corrective paths for the teeth often involvesvarious orthodontic measurements and diagnostics. Many of thesemeasurements utilize reference objects such as the occlusal plane, archform, and a tooth's local occlusal plane. Thus, accurate and reliableconstruction of these reference objects is an important step in theplanning of orthodontic treatment. Automatic construction of thesereference objects would save time and eliminate human error, thusimproving the accuracy of the dental measurements

SUMMARY OF THE INVENTION

System and method for automatic construction of orthodontic referenceobjects, such as the occlusal plane, arch form, and the local occlusalplane for a patient's teeth are disclosed. In accordance with anexemplary embodiment, a computer-implemented system and method forautomatic construction of the occlusal plane comprises receiving threedimensional data for the teeth, setting an initial direction for anormal of the occlusal plane, determining tips for selected teeth,calculating a plane that matches the determined tips, determining a newnormal for the calculated plane, and repeating the steps to calculate anew plane until the difference between planes in consecutive steps issmaller than a configurable parameter.

In accordance with an exemplary embodiment, a computer-implementedsystem and method for automatic construction of the arch form comprisesreceiving three dimensional data for the patient's teeth, detectingfacial axis points for the teeth, creating a plurality of pairs ofcorresponding teeth, calculating a mid-point for each created pair ofteeth, calculating a line that approximates the calculated mid-points,utilizing the calculated line as a y-axis of a coordinate frame of thearch form, utilizing a normal of an occlusal plane as a z-axis of thecoordinate frame of the arch form, determining an origin of thecoordinate frame of the arch form, determining an x-axis of thecoordinate frame by calculating a cross product of the y-axis and z-axisof the coordinate frame of the arch form, transforming each of thedetected facial axis points into the calculated coordinate frame of thearch form, and constructing control points of a Bezier spline curve fromthe transformed facial axis points.

In accordance with an exemplary embodiment, a computer-implementedsystem and method for automatic construction of the local occlusal planefor a tooth comprises receiving three dimensional data for the tooth,setting an initial direction for a normal of the local occlusal plane,determining a tip in the direction of the normal of the local occlusalplane for each of a quadrant of the tooth, calculating a plane thatmatches the determined tips, determining a new normal for the calculatedplane, and repeating the steps to calculate a new plane until thedifference between planes in consecutive steps is smaller than aconfigurable parameter.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present invention may be derived byreferring to the detailed description and claims when considered inconnection with the drawing Figures, where like reference numbers referto similar elements throughout the Figures, and:

FIGS. 1A, 1B, and 1C are diagrams showing the arrangement of a patient'steeth at an initial stage, an intermediate stage, and a final stage,respectively, of orthodontic treatment;

FIG. 1D is a diagram showing teeth numbering according to the standardsystem of tooth numbering;

FIG. 2 is a diagram illustrating a partial model of a patient'sdentition, including a model of gingival tissue;

FIG. 3 illustrates an exemplary occlusal plane in accordance with anembodiment of the present invention;

FIG. 4 illustrates an exemplary process for automatic construction ofthe occlusal plane in accordance with an embodiment of the presentinvention;

FIG. 5A illustrates a first exemplary arch form in accordance with anembodiment of the present invention;

FIG. 5B illustrates a second exemplary arch form in accordance with anembodiment of the present invention;

FIG. 6 illustrates a representative Bezier spline curve that representsan exemplary arch form in accordance with an embodiment of the presentinvention;

FIG. 7 illustrates a representative Bezier spline curve that representsan exemplary arch form in accordance with an embodiment of the presentinvention;

FIG. 8 illustrates an exemplary process for automatic construction ofthe arch form in accordance with an embodiment of the present invention;

FIG. 9 illustrates an exemplary process for automatic construction of alocal occlusal plane in accordance with an embodiment of the presentinvention;

FIG. 10 illustrates an exemplary occlusal plane in accordance with anembodiment of the present invention;

FIGS. 11A, 11B illustrate a representative Bezier spline curve thatrepresents an exemplary arch form in accordance with an embodiment ofthe present invention; and

FIG. 12 illustrates an exemplary local occlusal plane in accordance withan embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention may be described herein in terms of variouscomponents and processing steps. It should be appreciated that suchcomponents and steps may be realized by any number of hardware andsoftware components configured to perform the specified functions. Forexample, the present invention may employ various electronic controldevices, visual display devices, input terminals and the like, which maycarry out a variety of functions under the control of one or morecontrol systems, microprocessors or other control devices. In addition,the present invention may be practiced in any number of orthodonticcontexts and the exemplary embodiments relating to a system and methodfor automatic detection of dental features are merely a few of theexemplary applications for the invention. For example, the principles,features and methods discussed may be applied to any orthodontictreatment application.

U.S. patent application Ser. Nos. 09/264,547 and 09/311,716, now U.S.Pat. No. 6,514,074 describe techniques for generating 3-dimensionaldigital data sets containing models of individual components of apatient's dentition. These data sets include digital models ofindividual teeth and the gingival tissue surrounding the teeth.Furthermore, these applications also describe computer-implementedtechniques for using the digital models in designing and simulating anorthodontic treatment plan for the patient. For example, one suchtechnique involves receiving an initial data set that represents thepatient's teeth before treatment, specifying a desired arrangement ofthe patient's teeth after treatment, and calculating transformationsthat will move the teeth from the initial to the final positions overdesired treatment paths. U.S. patent application Ser. No. 09/169,276also describes the creation of data sets representing the toothpositions at various treatment stages and the use of these data sets toproduce orthodontic appliances that implement the treatment plan. Onetechnique for producing an orthodontic appliance involves creating apositive mold of the patient's dentition at one of the treatment stagesand using a conventional pressure molding technique to form theappliance around the positive mold. A design of orthodontic appliancesfrom the digital dentition models is, for example, described in U.S.patent application Ser. No. 09/169,034.

FIGS. 1A, 1B, and 1C show a patient's dentition at three stages during acourse of treatment. FIG. 1A illustrates the initial positions of thepatient's teeth before treatment begins. A digital model of the teeth atthese initial positions is captured in an initial digital data set(IDDS).

Such an IDDS may be obtained in a variety of ways. For example, thepatient's teeth may be scanned or imaged using well known technology,such as X-rays, three-dimensional x-rays, computer-aided tomographicimages or data sets, magnetic resonance images, and the like.

Methods for digitizing such conventional images to produce data sets arewell known and described in the patent and medical literature. By way ofexample, one approach is to first obtain a plaster cast of the patient'steeth by well known techniques, such as those described in Graber,Orthodontics: Principle and Practice, Second Edition, Saunders,Philadelphia, 1969, pp. 401-415. After the tooth casting is obtained, itcan be digitally scanned using a conventional laser scanner or otherrange acquisition system to produce the IDDS. The data set produced bythe range acquisition system may, of course, be converted to otherformats to be compatible with the software which is used formanipulating images within the data set. General techniques forproducing plaster casts of teeth and generating digital models usinglaser scanning techniques are described, for example, in U.S. Pat. No.5,605,459. In accordance with another exemplary embodiment, theacquiring of a digital model of a patient's teeth can also comprise suchtechniques as disclosed in U.S. Pat. No. 6,767,208, entitled “System andMethod for Positioning Teeth”, assigned to Align Technology, Inc.Accordingly, any methodology or process for converting scanned data intoa digital representation or otherwise for the acquiring of a digitalmodel of a patient's teeth can be utilized.

FIG. 1B illustrates an example of how the patient's teeth may beoriented at an intermediate stage in the treatment process, and FIG. 1Cillustrates an example of how the patient's teeth may be oriented attheir final positions. A human operator and/or a computer programmanipulate the digital models of the patient's teeth to prescribe thefinal tooth positions. The program then calculates one or more of theintermediate positions, taking into account any constraints imposed onthe movement of the teeth by the human operator or by the naturalcharacteristics of the teeth themselves. The program also accounts forany collisions that might occur between teeth as the teeth move from onetreatment stage to the next. Selecting the final and intermediate toothpositions and the treatment paths along which the teeth move isdescribed in more detail in one or more of the Patent Applicationsdiscussed above, which are all hereby incorporated by reference, intheir respective entireties.

FIG. 1D is a diagram of a set of teeth showing the standard system ofnumbering teeth. Reference is made to this standard system of numberingthroughout the discussion below.

FIG. 2 is a diagram illustrating a portion of a typical digitaldentition model 110 derived from the IDDS. Dentition model 110 includesmodels of individual teeth 120 and a model of the patient's gums 140.Various techniques for creating models of gum tissue and individualteeth from the IDDS are described in, for example, U.S. patentapplication Ser. Nos. 09/264,547 and 09/311,941.

Furthermore, FIG. 2 shows a portion of another gingival model 200 (a“secondary” gingival model), which is constructed to overlie gingivalmodel 140 derived from the IDDS (the “primary” gingival model). Theprogram uses the secondary gingival model 200 to model the deformationof the gingival tissue around the patient's teeth as the teeth move fromtheir initial positions to their final positions. This ensures thatorthodontic appliances made from positive molds of the patient'sdentition fit comfortably around the patient's gums at all treatmentstages. The secondary gingival model 200 also adds thickness to the gummodel, which ensures that the orthodontic appliances do not press tootightly against the patient's gums.

Reference will now be made to various exemplary embodiments of theinvention, which are illustrated in the accompanying figures. Whilethese exemplary embodiments are described in sufficient detail to enablethose skilled in the art to practice the invention, it should beunderstood that other embodiments may be realized and that logicaland/or mechanical changes may be made without departing from the spiritand scope of the invention. Thus, the various embodiments herein arepresented for purposes of illustration and not by way of limitation. Forexample, the steps recited in any of the method or process descriptionsmay be executed in any order and are not limited to the order presented.Moreover, any of the functions or steps may be outsourced to orperformed by one or more third parties.

For the sake of brevity, conventional data networking, applicationdevelopment, and other functional aspects of the systems (and componentsof the individual operating components of the systems) may not bedescribed in detail herein. Furthermore, the connecting lines shown inthe various figures contained herein are intended to represent exemplaryfunctional relationships and/or physical connections between the variouselements. It should be noted that many alternative and/or additionalfunctional relationships or physical connections may be present in apractical system.

Various embodiments of the present invention include one or morecomputing devices having programs stored therein for staging themovement of a patient's teeth. The computing device(s) or variouscomponents of any computing device discussed herein may include one ormore of the following: a host server or other computing systemsincluding a processor for processing digital data; a memory coupled tothe processor for storing digital data; an input digitizer coupled tothe processor for inputting digital data; an application program storedin the memory and accessible by the processor for directing processingof digital data by the processor; a display device coupled to theprocessor and memory for displaying information derived from digitaldata processed by the processor; and a plurality of databases. Variousfile indexes and/or databases used herein may include: client data;merchant data; and/or other similar useful data.

As those skilled in the art will appreciate, any computing deviceutilized by a user may include an operating system (e.g., Windows NT,95/98/2000, OS2, UNIX, Linux, Solaris, MacOS, etc.) as well as variousconventional support software and drivers typically associated withcomputers. As will be appreciated by one of ordinary skill in the art,each computing device may be embodied as a customization of an existingsystem, an add-on product, upgraded software, a stand alone system, adistributed system, a method, a data processing system, a device fordata processing, and/or a computer program product. Accordingly, anyprogram stored therein may take the form of an entirely softwareembodiment, an entirely hardware embodiment, or an embodiment combiningaspects of both software and hardware. Furthermore, any program may takethe form of a computer program product on a computer-readable storagemedium having computer-readable program code means embodied in thestorage medium. Any suitable computer-readable storage medium may beutilized, including hard disks, CD-ROM, optical storage devices,magnetic storage devices, and/or the like.

In accordance with one exemplary embodiment, a computing device isconfigured to receive an electronic representation of the patient'steeth in an initial position taken by, for example, an intra-oralscanner or a CT scanner based on an impression or partial impression ofthe patient's teeth. The received data includes three dimensional datafor the patient's teeth that can be used as input into the variousembodiments of the present invention for automatic detection of theteeth's features. In addition, the computing device is configured toreceive or generate an electronic representation of a desired finalposition for each of the patient's teeth. The program stored within thecomputing device is configured to analyze the initial and finalpositions, and automatically create a route for each tooth to move fromits initial position to its final position. A set of aligners to movethe teeth along the path in various stages is manufactured for thepatient. As the patient wears the aligners, the patient's teeth movealong the path according to each stage.

In order to analyze the initial, intermediate and final positions of theteeth, various orthodontic measurements and diagnostics are taken thatutilize reference objects such as the occlusal plane, the arch form forthe upper and lower jaw, and the local occlusal plane for specificteeth, such as the molars. Measurements of these reference objects areused to determine the corrective path for moving the patient's teeth,and can also be used to determine the final position of the teeth. Inorder to assist these measurements, the present invention provides forautomatic construction of various orthodontic reference objects, such asthe occlusal plane, arch form, and the local occlusal plane for a tooth.

With reference to FIGS. 3 and 10, in accordance with one embodiment ofthe present invention, the occlusal plane 300 is the imaginary surfacewhere the upper teeth and the lower teeth meet. For a normal bite,occlusal plane 300 will pass through the tips of lower jaw second molars310 and the central incisors 320.

In accordance with one embodiment of the present invention, anorthogonal (i.e., x,y,z) frame of reference is used where the x-axis isaligned in the buccal-lingual direction, which is the direction betweenthe cheek and tongue. The y-axis is aligned in the mesial-distaldirection, which is the direction between the front of the mouth and theback of the mouth. The z-axis is aligned in the occlusal-root direction,which is the direction from the top of a tooth to the part of the toothin the gum. It will be appreciated that in other embodiments of thepresent invention, the x-axis, y-axis, and z-axis, may be interchangedwith each other or may be aligned in other orientations.

FIG. 4 is a flow diagram illustrating an exemplary process 400 forautomatic construction of the occlusal plane comprising setting aninitial direction for the occlusal plane normal (410), determining thetip of each of the first molars and central incisors of the lower jaw inthe direction of the occlusal plane normal (420), calculating a planethat best fits the tips from step 420 (430), determining a new normal tothe calculated plane from step 430 (440), repeating steps 420-440 withthe new occlusal plane normal until the variation of the plane issmaller than a configurable parameter. This and other configurableparameters may be read from a computer file (e.g., parameter file) ormay be entered by user in response to one or more prompts from thecomputer program. In accordance with one embodiment of the presentinvention, the z-axis is used as the initial direction of the occlusalplane normal (410). The direction of the z-axis corresponds to thedirection between the top of a tooth (such as one of the lower jawsecond molars) and the part of the tooth in the gum. In accordance withother embodiments of the present invention, the occlusal plane normalmay have a different initial setting.

As mentioned above, input data is received in the form of threedimensional data that represents the initial position of the teeth. Foreach of the lower jaw first molars and central incisors, the tip of eachtooth may be determined by surveying the three dimensional data anddetermining the highest vertex in the direction of the current occlusalplane normal (420). This will result in a set of points that representthe highest vertex for each of the teeth that have been examined. Inaccordance with other embodiments of the present invention, teeth otherthan the lower jaw first molar and central incisors may be used tocalculate the occlusal plane. For example, the lower jaw second molarsmay be used instead of, or in addition to the lower jaw first molars.Configurable parameters to the computer program can be used to specifythe particular teeth that are to be used for calculation of the occlusalplane.

Next, a plane is calculated that best matches the set of points (430)utilizing a best fit or similar method. A new occlusal plane normal canbe calculated from the plane (440). Using the new occlusal plane normal,steps 420-440 are repeated with the new occlusal plane normal, until thevariation between the planes in consecutive steps is smaller than aconfigurable parameter.

With reference to FIG. 5A, in accordance with one embodiment of thepresent invention, an arch form 500 is the shape of the arch of theteeth in either the upper or lower jaw. For a normal bite, arch form 500has a smooth, symmetric appearance. With reference to FIG. 5B, in theexample of crowded or improperly located teeth, arch form 500 has ajagged, non-symmetric appearance. Many measurements such as toothrotation and prominence are based on the arch form curve.

In accordance with an exemplary embodiment of the present invention,arch form 500 is represented by a 2-segment Bezier spline curve thatpasses through the midpoints of the facial axes of the clinical crown(FACC), that is FA points of the teeth. Each segment of the Bezierspline curve is a cubic curve with four control points. With referenceto FIGS. 6-7 and 11A-B, a representative 2-segment Bezier spline curve600 is illustrated that represents an exemplary arch form that passesthrough FA points 710. In the example of FIG. 6, Bezier spline curve 600is constructed from two segments 612, 614. Control points 610, 620, 630,640 are used to construct segment 612, and control points 640, 650, 660,670 are used to construct segment 614. Bezier spline curve 600 is formedby approximating a curve that passes through control points 610-670.

As mentioned above, input data is received in the form of threedimensional data that represents the initial position of the teeth. FIG.8 is a flow diagram illustrating an exemplary process for automaticconstruction of the arch form. In accordance with one embodiment of thepresent invention, utilizing the received three dimensional data, aprocess for automatic construction of the arch form includes detectingFA points for the teeth of the upper or lower jaw (810), creating pairsof corresponding teeth (820), calculating a mid-point for each pair ofteeth (830), calculating a line that approximates the calculatedmid-points (840), utilizing the calculated line as the y-axis of acoordinate frame of the arch form (850), utilizing the normal vector tothe occlusal plane 300 as the z-axis of the coordinate frame of the archform (860), determining the mid-point of the second molars for theorigin of the coordinate frame of the arch form (870), using the crossproduct of the y-axis and z-axis for the x-axis of the coordinate frameof the arch form (880), transforming each of the detected FA points intothe calculated coordinate frame of the arch form (890), and using aleast square algorithm to determine the control points of the Bezierspline curve of the arch form (895).

FA points are detected (810) for the teeth of either the upper or lowerarch. In accordance with one embodiment of the present invention, FApoints may be detected by determining the Facial Axis centers for allcrowns of teeth.

Pairs of corresponding teeth are created (820) for teeth on the left andright side of the arch. For example, the left second molar is pairedwith the right second molar. For each pair of teeth, a mid-point of aline between the teeth is calculated (830). In accordance with oneembodiment of the present invention, the line between the FA points ofthe pair of teeth is used for calculating the mid-point. Otherembodiments of the present invention may utilize other parts of theteeth such as the tips of the teeth.

Next, a line is calculated that approximates the calculated mid-points(840). The calculated line may treat each calculated mid-point equally,or certain of the mid-points may be weighted such that the weightedmid-points have more of an effect on the final location of the line.This line may be used as the y-axis of a coordinate frame of the archform (850). In accordance with other embodiments of the presentinvention, the line may be used as another axis of the arch form such asthe x-axis or z-axis.

The normal to occlusal plane 300 may be used as the z-axis of thecoordinate frame of the arch form (860). Similarly, in accordance withother embodiments of the present invention, the normal to occlusal plane300 may be used as another axis of the arch form such as the x-axis ory-axis.

The middle point for the second molars may be used as the origin of thecoordinate frame (870). That is, the mid-point for a line connecting theFA points of the second molars may be used as the origin of thecoordinate frame of the arch form. Other embodiments of the presentinvention may utilize the mid-point of the line connecting the tips ofthe second molars as the origin of the coordinate frame. Otherembodiments may utilize the mid-point of the line connecting the firstmolars as the origin of the coordinate frame of the arch form.

The x-axis of the coordinate frame may be determined from the crossproduct of the y-axis and the z-axis (step 880).

All FA points are transformed into the newly calculated x-y-z coordinateframe (step 890) such that the FA points are in the same coordinatesystem of the constructed arch form. Finally, a least square algorithmmay be used to find the control point of Bezier spine curve (895) fromthe transformed FA points. As stated above, the calculated Bezier spinecurve represents the arch form for the teeth of the arch.

FIG. 9 is a flow diagram illustrating an exemplary process 900 forautomatic construction of a local occlusal plane for a tooth such as afirst or second molar. An exemplary process comprises setting an initialdirection for the local occlusal plane normal (910), determining thetip, in the direction of the local occlusal plane normal, for each ofthe four quadrants defined by the tooth frame of reference (920),calculating a plane that best fits the tips (930), calculating a normalof the calculated plane, and repeating steps 920-940 with the new localocclusal plane normal until the variation of the plane is smaller than aconfigurable parameter. In accordance with one embodiment of the presentinvention, the vertical axis of the tooth is used as the initialdirection of the local occlusal plane normal (910). The vertical axiscorresponds to the direction between the top of the tooth to the part ofthe tooth in the gum. In accordance with other embodiments of thepresent invention, the occlusal plane normal may have a differentinitial setting.

With reference to FIG. 12, for each of the four quadrants of the tooth,the tip of each quadrant may be determined by surveying the threedimensional data and determining the highest vertex in the direction ofthe current local occlusal plane normal (920). This will result in a setof points that represent the highest vertex for each quadrant of thetooth being examined.

Next, a plane is calculated that best matches the set of tips (930)utilizing a means square approach or similar method. A new localocclusal plane normal can be calculated from the plane (940). Using thenew local occlusal plane normal, steps 920-940 are repeated with the newlocal occlusal plane normal, until the variation between the planes onconsecutive steps is smaller than a configurable parameter.

Benefits, other advantages, and solutions to problems have beendescribed herein with regard to specific embodiments. However, thebenefits, advantages, solutions to problems, and any element(s) that maycause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as critical, required, or essentialfeatures or elements of any or all the claims or the invention. Thescope of the present invention is accordingly to be limited by nothingother than the appended claims, in which reference to an element in thesingular is not intended to mean “one and only one” unless explicitly sostated, but rather “one or more.” All structural, chemical, andfunctional equivalents to the elements of the above-described exemplaryembodiments that are known to those of ordinary skill in the art areexpressly incorporated herein by reference and are intended to beencompassed by the present claims.

1. A computer-implemented method for automatic construction of occlusalplanes for a patient's teeth, comprising: a) receiving three dimensionaldata for a patient's teeth; b) setting an initial direction fordetermining a tip of more than one tooth, the initial direction being avertical axis of a selected one of the patient's teeth between a top ofthe selected one of the patient's teeth and a root of the selected oneof the patient's teeth in the patient's gums; c) determining a tip,based on the initial direction, for each of a first molar and a centralincisor of a lower jaw of the patient's teeth; d) calculating anocclusal plane that best fits the determined tips; e) determining anormal for the calculated occlusal plane; f) determining a new tip,based on the normal, for each of the first molar and the central incisorof the lower jaw of the patient's teeth; and g) calculating a newocclusal plane that best fits the determined new tips; wherein steps(a)-(g) are performed by a computer.
 2. The computer-implemented methodof claim 1, wherein the step of setting the initial direction comprisesusing a z-axis as the initial direction.
 3. The computer-implementedmethod of claim 2, wherein the z-axis corresponds to a direction betweenthe top of the one of the patient's teeth and the root of the one of thepatient's teeth.
 4. The computer-implemented method of claim 1, whereinthe step of determining the tip comprises: examining the threedimensional data for each of the first molars and for each of thecentral incisors of the lower jaw of the patient's teeth; anddetermining a highest point for each of the examined teeth in theinitial direction.
 5. The computer-implemented method of claim 4,wherein each of a second molar are examined instead of each of the firstmolars.
 6. The computer-implemented method of claim 4, wherein each of asecond molar are examined in addition to each of the first molars. 7.The computer-implemented method of claim 1, wherein a tip is determinedfor each of a first molar and a central incisor of an upper jaw of thepatient's teeth instead of the lower jaw.
 8. The computer-implementedmethod of claim 1, wherein the method further includes: h) determining anew normal for the calculated new occlusal plane.
 9. Thecomputer-implemented method of claim 8, wherein the method includesrepeating at least steps (f)-(g).
 10. The computer-implemented method ofclaim 8, further comprising repeating steps (f)-(h) until a variationbetween the new occlusal plane and the determined new tips is smallerthan a configurable parameter.
 11. A computerized system for automaticconstruction of occlusal planes for a patient's teeth, the computerizedsystem comprising: a microprocessor comprising a plurality ofalgorithms; a memory device; and wherein the computerized system isconfigured for: a) receiving three dimensional data for a patient'steeth; b) setting an initial direction for determining a tip of morethan one tooth, the initial direction being a vertical axis of aselected one of the patient's teeth between a top of the selected one ofthe patient's teeth and a root of the selected one of the patient'steeth in the patient's gums; c) determining a tip, based on the initialdirection, for each of a first molar and a central incisor of a lowerjaw of the patient's teeth; d) calculating an occlusal plane that bestfits the determined tips; e) determining a normal for the calculatedocclusal plane; f) determining a new tip, based on the normal, for eachof the first molar and the central incisor of the lower jaw of thepatient's teeth; and g) calculating a new occlusal plane that best fitsthe determined new tips.
 12. The computerized system of claim 11,wherein a tip is determined for each of a first molar and a centralincisor of an upper jaw of the patient's teeth instead of the lower jaw.13. The computerized system of claim 11, wherein the computerized systemis further configured for: h) determining a new normal for thecalculated new occlusal plane.
 14. The computerized system of claim 13,wherein the computerized system is further configured for repeating atleast steps (f)-(g).
 15. The computerized system of claim 13, whereinthe computerized system is further configured for repeating steps(f)-(h) until a variation between the new occlusal plane and thedetermined new tips is smaller than a configurable parameter.